3(x-1)-18=x(x-1)-3(3x+1)

Solution for 3(x-1)-18=x(x-1)-3(3x+1) equation:

Simplifying
3(x + -1) + -18 = x(x + -1) + -3(3x + 1)

Reorder the terms:
3(-1 + x) + -18 = x(x + -1) + -3(3x + 1)
(-1 * 3 + x * 3) + -18 = x(x + -1) + -3(3x + 1)
(-3 + 3x) + -18 = x(x + -1) + -3(3x + 1)

Reorder the terms:
-3 + -18 + 3x = x(x + -1) + -3(3x + 1)

Combine like terms: -3 + -18 = -21
-21 + 3x = x(x + -1) + -3(3x + 1)

Reorder the terms:
-21 + 3x = x(-1 + x) + -3(3x + 1)
-21 + 3x = (-1 * x + x * x) + -3(3x + 1)
-21 + 3x = (-1x + x2) + -3(3x + 1)

Reorder the terms:
-21 + 3x = -1x + x2 + -3(1 + 3x)
-21 + 3x = -1x + x2 + (1 * -3 + 3x * -3)
-21 + 3x = -1x + x2 + (-3 + -9x)

Reorder the terms:
-21 + 3x = -3 + -1x + -9x + x2

Combine like terms: -1x + -9x = -10x
-21 + 3x = -3 + -10x + x2

Solving
-21 + 3x = -3 + -10x + x2

Solving for variable 'x'.

Reorder the terms:
-21 + 3 + 3x + 10x + -1x2 = -3 + -10x + x2 + 3 + 10x + -1x2

Combine like terms: -21 + 3 = -18
-18 + 3x + 10x + -1x2 = -3 + -10x + x2 + 3 + 10x + -1x2

Combine like terms: 3x + 10x = 13x
-18 + 13x + -1x2 = -3 + -10x + x2 + 3 + 10x + -1x2

Reorder the terms:
-18 + 13x + -1x2 = -3 + 3 + -10x + 10x + x2 + -1x2

Combine like terms: -3 + 3 = 0
-18 + 13x + -1x2 = 0 + -10x + 10x + x2 + -1x2
-18 + 13x + -1x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
-18 + 13x + -1x2 = 0 + x2 + -1x2
-18 + 13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + 13x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
18 + -13x + x2 = 0

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -13x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -13x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -13x + x2 = 0 + -18
-13x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-13x + x2 = -18

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -18 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -18 + 42.25

Combine like terms: -18 + 42.25 = 24.25
42.25 + -13x + x2 = 24.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + -6.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
x + -6.5 = 4.924428901

Simplifying
x + -6.5 = 4.924428901

Reorder the terms:
-6.5 + x = 4.924428901

Solving
-6.5 + x = 4.924428901

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 4.924428901 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 4.924428901 + 6.5
x = 4.924428901 + 6.5

Combine like terms: 4.924428901 + 6.5 = 11.424428901
x = 11.424428901

Simplifying
x = 11.424428901

Subproblem 2
x + -6.5 = -4.924428901

Simplifying
x + -6.5 = -4.924428901

Reorder the terms:
-6.5 + x = -4.924428901

Solving
-6.5 + x = -4.924428901

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -4.924428901 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -4.924428901 + 6.5
x = -4.924428901 + 6.5

Combine like terms: -4.924428901 + 6.5 = 1.575571099
x = 1.575571099

Simplifying
x = 1.575571099

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.424428901, 1.575571099}